Yes, they did split it up poorly, the entire region maybe. But eh, splitting up the middle-east could probably never have been done 'right'.
Do the Kurdish people or rebel groups really attack villages or targets in Turkey?
No, but PKK does, more terrorist than just rebel according to most.
There's no oil as far as I know, only oil pipeline running through eastern Turkey to the sea... coming from Kazachstan I think. As far as Northern Iraq, not much I think, it's why splitting Iraq in three wouldn't work...one or two will be left without oil.
The Turkish government first of all is afraid of the Iraqi situation getting out of hand and the fight moving into Turkey. This would be insurgency, not a battlefield, doesn't matter how it would compare to the Turkish military. Huge political issues. Secondly there's the PKK which alledgely uses Northern Iraq as base now.
I think couple of days ago, Turkish jets and artillery bombarded some villages/targets in Northern Iraq, said to be aimed at PKK.
Now, I'll shut up now, because it's highly political and I don't know much about it either.